A Conservative spokesman had said all the calls were compliant with the law.

Labour MP Wayne David said South Wales Police were looking into the claims.

Speaking in the Commons on Thursday, Mr David said the Electoral Commission had written to him confirming the police were "formally considering the allegations".

An undercover investigation by C4 News, broadcast last month, claimed call centre workers may have been carrying out paid canvassing, banned under electoral law, as they promoted key Conservative messages to undecided voters in the weeks before the election.

The investigation claimed that calls were made to voters in key marginal seats, including Bridgend, Gower, Clwyd South and Wrexham.

At the start of the election campaign, the information commissioner, Elizabeth Denham, contacted all parties to remind them of the law around direct marketing.

At the time a Conservative spokesman said: "All the scripts supplied by the party for these calls are compliant with data protection and information law".

Caerphilly MP Mr David told BBC Wales that he would be speaking with South Wales Police in the next few days to establish the nature and scope of the inquiry.